Three dimensional (3D) fluorescence microscopy is a powerful tool for the study of living specimens. 3D images are normally obscured by out-of-focus blur and often artifactual due to the limited band of spatial frequencies that the conventional fluorescence microscope can image. These problems can be ameliorated by optical and/or computational methods. A recent renaissance in optical microscopy has led to a wide variety of approaches to overcome the out-of-focus blur and band-limitation (confocal and partially confocal scanning, 2- and 3-photon fluorescence excitation, standing wave, structured-fluorescence-excitation microscopes..). These approaches improve the imaging properties, but they are not blur-free and computational approaches further improve image quality. Computational methods have gained acceptance as an alternative or complement to optical methods, but their development has not enjoyed the fast pace of their optical counterparts. Few commercially-available deconvolution packages exist, and most are based on the first few algorithms developed for 3D deconvolution, including ad-hoc and unconstrained methods unable compensate for the band-limitation of microscopes. Significant improvements are possible with methods based on a thorough mathematical model of the process of image formation and recording. The long-term goals of the proposed research are: 1) To further develop computational algorithms that account for the most significant sources of degradation in the image. 2) To develop computational image estimation methods for the newly-developed structured illumination microscope. 3) To provide guidelines for the use of the algorithms and for their capabilities and limitations. To achieve this goal we will first derive algorithms based on an accurate model for the microscope and light detector then we will do a thorough evaluation of these and other algorithms to assess their relative merits and to provide guidelines for their use.